BAGHDAD, Iraq (CNN) -- Iraqi lawmakers expect to get a chance Thursday to break a major political impasse and vote on a Cabinet proposed by Prime Minister-designate Ibrahim al-Jaafari.

Al-Jaafari told a press conference Wednesday that he had submitted his proposed Cabinet to President Jalal Talabani, who must approve the names before the transitional National Assembly votes on them.

Al-Jaafari's announcement came a short time after gunmen shot and killed an assembly member on her doorstep in Baghdad -- the first top lawmaker assassinated since the legislative body was voted into power January 30.

Lamee'a Abd Khidawi, a member of outgoing Prime Minister Ayad Allawi's legislative bloc, was shot to death when she answered the door to her house, Baghdad emergency police said. No one has claimed responsibility.

He said the step will help erase the sins of the past, bringing stability and hope to Iraqis.

"We want to return the smiles to the faces of the children," he said.

Politicians have had difficulty finding common ground in the three months since 8 million Iraqis risked their lives to go to the polls.

In jockeying for power, lawmakers have been trying to satisfy the needs of their supporters and other groups that want to be represented in key government positions.

The Shiite Muslim-led United Iraqi Alliance came out on top in the January elections, while the Kurdish bloc placed second and Allawi's Iraqi List party was third. Talabani is a Kurd, and al-Jaafari is a Shiite.

More bodies found in Tigris

The Polish-led command in Iraq said Wednesday that police had found the bodies of a Najaf police official and another person in the Tigris River.

Kadhum was abducted earlier this month when he was in the southern Baghdad area of Dura, the Iraqi government has said.

The bodies were found in the vicinity of Suwayra -- the same area where police found 57 bodies last week.

Other developments

The U.S. military and Iraqi security forces have arrested 36 suspected insurgents and found three weapons caches in the northern cities of Mosul and Tal Afar, the military said Wednesday.

Iraq is offering a $1 million reward for information leading to the arrest of al-Baqi abd al-Karim al-Abdallah al-Sadun, a former high-ranking member of Saddam Hussein's Baath Party. The government accuses al-Sadun of funding insurgents in eastern and central Iraq and supervising the torture and killing of about 500 civilians in 1991.

U.S. Defense Secretary Donald Rumsfeld, appearing before senators Wednesday, defended the number of U.S. troops in Iraq. He told a Senate panel discussing the military's budget that U.S. generals have told the Pentagon the number of troops they believe is necessary and said: "I believe they're right."

Koichiro Matsuura, the top official for the United Nations Educational, Scientific and Cultural Organization, has called on "authorities and on all the warring factions in Iraq to respect the safety of journalists." An Associated Press cameraman was killed over the weekend and three Romanian journalists remain hostages in Iraq. Reporters without Borders said 55 journalists and media assistants have been killed since the war began more than two years ago.